Conformal Designs based on Vertex Operator Algebras

Details Conformal Designs based on Vertex Operator Algebras Conformal Designs based on Vertex Operator Algebras

2007-01-23

arxiv.org/abs/math/0701626v1

Mathematics

Quantum Algebra

35 pages with 1 table, LaTeX

Scientific paper

We introduce the notion of a conformal design based on a vertex operator algebra. This notation is a natural analog of the notion of block designs or spherical designs when the elements of the design are based on self-orthogonal binary codes or integral lattices, respectively. It is shown that the subspaces of fixed degree of an extremal self-dual vertex operator algebra form conformal 11-, 7-, or 3-designs, generalizing similar results of Assmus-Mattson and Venkov for extremal doubly-even codes and extremal even lattices. Other examples are coming from group actions on vertex operator algebras, the case studied first by Matsuo. The classification of conformal 6- and 8-designs is investigated. Again, our results are analogous to similar results for codes and lattices.

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